Answered

At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Join our platform to connect with experts ready to provide detailed answers to your questions in various areas. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

the sum of any n consecutive integers is always equal to 100 less than the sum of the next n consecutive integers. Find n.

Sagot :

facundo3141592

When we have a given number k, the consecutive number to k will be (k + 1), the next consecutive will be (k + 2), and so on.

With this, we can find that the value of n is 100.

So here we have n consecutive numbers, let's assume we start with the number k, then the sum will be:

k + (k + 1) + ... + (k + n - 1)

Now we know that this is 100 less than the sum of the next n consecutive numbers.

For the next n consecutive numbers we need to start at k + 1, then we get:

(k + 1) + (k + 2) + ... + (k + n - 1) + (k + n)

If we take the difference we will get:

((k + 1) + (k + 2) + ... + (k + n - 1) + (k + n)) - (k + (k + 1) + ... + (k + n - 1)) = 100

As you can see, there are a lot of terms that are in both parentheses, then when we do that difference a lot of them cancel out.

So we will et:

((k + 1) + (k + 2) + ... + (k + n - 1) + (k + n)) - (k + (k + 1) + ... + (k + n - 1))

= (k + n) - k = k + n - k = n

And we knew that this difference must be equal to 100, then we have:

n = 100

We just found the value of n.

If you want to learn more, you can read:

https://brainly.com/question/1767889

We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.